A new approach using hybrid power series – cuckoo search optimization algorithm to solve electrostatic pull-in instability and deflection of nano cantilever switches subject to van der waals attractions

  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract

    A hybrid Power Series (PS) and Cuckoo Search via L´evy Flights (CS) optimization algorithm (PS-CS) method is utilized to obtain a solution for the deflection and pull-in instability of a nano cantilever switch in the presence of the van der Waals attractions, electrostatic forces and fringing filed effects. In order to obtain a relation for deflection of the beam, a trial solution including adjustable coefficients, satisfying the boundary conditions of the governing, is proposed. The cuckoo search optimization algorithm is executed to find the ad-justable parameters of the trial solution satisfying the governing equation of the nanobeam. The results are compared with the available results in the literature as well as numerical solution. The results indicate the remarkable accuracy of the present approach. The minimum initial gap and the critical free standing detachment length of the nano actuator that does not stick to the substrate due to the van der Waals attractions, as an important parameter in pull-in instability of the nano switches, is calculated. Utilizing the results of the PS-CS, the stress distribution inside the nano actuator is determined at the onset of the pull-in instability.

  • Keywords

    Cantilever Nano Actuator; Pull-In Instability; Electromechanical Switches.

  • References

      [1] Sinha, N., Wabiszewski, G. E., Mahameed, R., Felmetsger, V. V., Tanner, S. M., Carpick, R. W., & Piazza, G. (2009, June). Ultra thin AlN piezoelectric nano-actuators. In Solid-State Sensors, Actuators and Microsystems Conference, 2009. TRANSDUCERS 2009. International (pp. 469-472). IEEE. https://doi.org/10.1109/sensor.2009.5285460.

      [2] Cui, J. B., Sordan, R., Burghard, M., & Kern, K. (2002). Carbon nanotube memory devices of high charge storage stability. Applied Physics Letters, 81(17), 3260-3262. https://doi.org/10.1063/1.1516633.

      [3] Soroush A, Koochi A, Kazemi AS, Noghrehabadi A, Haddadpour H, Abadyan M. Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nano-actuators. J. Phys. Scr. 2010; 82 045801. https://doi.org/10.1088/0031-8949/82/04/045801.

      [4] Mastrangelo CH, CH Hsu, 1993 Mechanical stability and adhesion of microstructures under capillary force-Part I: Basic theory Journal of Microelectromechanical Systems 2 (1): 33-43 https://doi.org/10.1109/84.232593.

      [5] Lieber, C. M., Rueckes, T., Joselevich, E., Kim, K. (2001). Nanoscopic wire-based devices, arrays, and methods of their manufacture, Google Patents.

      [6] Wen-Hui Lin, and Ya-Pu Zhao, Pull-in Instability of Micro-switch Actuators: Model Review, International Journal of Nonlinear Sciences and Numerical Simulation, 9(2), 175-183, 2008 https://doi.org/10.1515/IJNSNS.2008.9.2.175.

      [7] Lin, W. H., & Zhao, Y. P. (2005). Casimir effect on the pull-in parameters of nanometer switches. Microsystem Technologies, 11(2-3), 80-85. https://doi.org/10.1007/s00542-004-0411-6.

      [8] Noghrehabadi, A., Ghalambaz, M., & Ghanbarzadeh, A. (2012). A new approach to the electrostatic pull-in instability of nanocantilever actuators using the ADM–Padé technique. Computers & Mathematics with Applications, 64(9), 2806-2815. https://doi.org/10.1016/j.camwa.2012.04.013.

      [9] Ramezani A, Alasty A, Akbari J., Closed-form approximation and numerical validation of the influence of van der Waals force on electrostatic cantilevers at nano-scale separations. Nanotechnology, 2008; 19 015501 (10pp).

      [10] Ramezani A, Alasty A, Akbari J., Closed-form solutions of the pull-in instability in nano-cantilevers under electrostatic and intermolecular surface forces. Int. J. Solids Struct. 2007; 44 4925–4941. https://doi.org/10.1016/j.ijsolstr.2006.12.015.

      [11] Meade Jr A.J., Fernandez A.A., The numerical solution of linear ordinary differential equations by feedforward neural networks, Mathematical and Computer Modelling. 1994; 19 (12): 1–25. https://doi.org/10.1016/0895-7177(94)90095-7.

      [12] Lagaris I.E., Likas A., Fotiadis D.I. Artificial neural networks for solving ordinary and partitial differential equations. IEEE Transactions on Neural Networks. 1998; 9 (5): 987–1000. https://doi.org/10.1109/72.712178.

      [13] Malek A., Beidokhti R.S., Numerical solution for high order differential equations using a hybrid neural network—Optimization method. Applied Mathematics and Computation. 2006; 183: 260-271. https://doi.org/10.1016/j.amc.2006.05.068.

      [14] Lee H., Kang I.S., Neural algorithms for solving differential equations, Journal of Computational Physics 1990; 91: 110–131. https://doi.org/10.1016/0021-9991(90)90007-N.

      [15] Yang X.-S., Deb S., “Cuckoo search via L´evy flights”, in: Proc. Of World Congress on Nature & Biologically Inspired Computing (NaBIC 2009), December 2009, India. IEEE Publications, USA, pp. 210-214 (2009). https://doi.org/10.1109/NABIC.2009.5393690.

      [16] Chaowanawatee, K., & Heednacram, A. (2012, July). Implementation of cuckoo search in RBF neural network for flood forecasting. In Computational Intelligence, Communication Systems and Networks (CICSyN), 2012 Fourth International Conference on (pp. 22-26). IEEE. https://doi.org/10.1109/cicsyn.2012.15.

      [17] Santos, C. A., Freire, P. K., & Mishra, S. K. (2012). Cuckoo search via Lévy flights for optimization of a physically-based runoff-erosion model. Journal of Urban and Environmental Engineering, 6(2), 123-131. https://doi.org/10.4090/juee.2012.v6n2.123131.

      [18] Valian, E., & Valian, E. (2013). A cuckoo search algorithm by Lévy flights for solving reliability redundancy allocation problems. Engineering Optimization, 45(11), 1273-1286 https://doi.org/10.1080/0305215X.2012.729055.

      [19] Kennedy J., Eberhart R.C., Particle swarm optimization. Proc. of IEEE International Conference on Neural Networks, Piscataway, NJ. pp. 1942-1948 (1995). https://doi.org/10.1109/ICNN.1995.488968.

      [20] Kennedy J., Eberhart R., Shi Y., Swarm intelligence, Academic Press, (2001).

      [21] Ascher U.; Mattheij, R., Russell, R. "Numerical Solution of Boundary Value Problems for Ordinary Differential Equations." SIAM Classics in Applied Mathematics. Vol. 13. (1995). https://doi.org/10.1137/1.9781611971231.

      [22] Ascher U., Petzold, L. "Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations." SIAM, Philadelphia. 1998. https://doi.org/10.1137/1.9781611971392.

      [23] Timoshenko S., Theory of Plates and Shells, (New York: McGraw Hill) 1987.




Article ID: 7488
DOI: 10.14419/ijet.v6i2.7488

Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.